An Explicit Total Lagrangian Fragile Points Method for Finite Deformation of Hyperelastic Materials

TL;DR

This paper introduces an explicit total Lagrangian Fragile Points Method (FPM), a meshless approach for simulating finite deformations of hyperelastic materials, demonstrating superior convergence and accuracy over FEM in large deformation scenarios.

Contribution

The paper presents a novel meshless FPM with explicit total Lagrangian formulation and simple one-point integration, improving accuracy and convergence in large deformation hyperelasticity simulations.

Findings

FPM maintains accuracy for large deformations where FEM fails.

FPM uses simple one-point integration for exact weak form integration.

FPM outperforms FEM in convergence during hyperelastic deformation simulations.

Abstract

This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods are more suitable for large deformation modelling since they use enriched shape functions for the approximation of displacements. However, this comes at the expense of extra computational overhead and higher-order quadrature is required to obtain accurate results. In this work, the novel meshless method FPM was used to derive an explicit total Lagrangian algorithm for finite deformation. FPM uses simple one-point integration for exact integration of the Galerkin weak form since it employs simple discontinuous polynomials as trial and test functions, leading to accurate results even with single-point quadrature. The proposed method was evaluated by comparing it with FEM in several case studies considering both the extension and compression of a hyperelastic material. It was demonstrated that FPM maintained good accuracy even for large deformations where FEM failed to converge.